Non-linear finite-amplitude oscillations of the large beam arrays oscillating in viscous fluids

Abstract

Over the past decade, several studies have been conducted on a single and multiple oscillating thin cantilever beams in an unbounded viscous fluid. With an increase in the applications of large array oscillators in a fluid environment for fields like medicine, biology, and energy harvesting devices, it is crucial to understand the nature of the surrounding fluid dynamics. In this present study, we perform a two-dimensional computational fluid dynamics (CFD) analysis of an array of beams oscillating in an unbounded viscous fluid. The two-dimensional Navier Stokes and continuity equations are solved to investigate the hydrodynamic forces exerted on the array members from interaction with the fluid environment. A complex hydrodynamic function is proposed here to represent the distributed hydrodynamic loading experienced by the oscillating beams. Results suggest that there is an increase in viscous damping with an increase in the size of the array. In addition, the nonlinearities become dominant when an array of beams is subjected to large amplitude oscillations. The number of beams in an array determines the overall hydrodynamics and the array effect. CFD analysis can predict the non-linearities unlike boundary integral method (BIM) approach, which is limited for low amplitudes. The results from the full Navier–Stokes simulations compared favorably with results using the BIM for the time-harmonic linearized Stokes equations.